Operations on Real Numbers MCQs Quiz | Class 9

This quiz covers Class IX Mathematics (Code 041), Unit I: Number Systems, focusing on Operations on Real Numbers. Test your understanding of addition, subtraction, multiplication, and division of real numbers, along with their properties like closure, commutative, associative, and distributive laws. Click Submit to see your score and download the answer PDF.

Operations on Real Numbers: Key Concepts

In Class 9 Mathematics, Unit I: Number Systems, operations on real numbers involve handling both rational and irrational numbers. Understanding how to add, subtract, multiply, and divide these numbers is essential for simplifying algebraic expressions and solving equations.

1. Properties of Operations

The operations on real numbers satisfy specific properties:

  • Closure Property: The sum or product of two real numbers is always a real number.
  • Commutative Laws: For addition (a + b = b + a) and multiplication (ab = ba).
  • Associative Laws: For addition (a + b) + c = a + (b + c) and multiplication (ab)c = a(bc).
  • Distributive Law: Multiplication distributes over addition: a(b + c) = ab + ac.

2. Operations with Roots (Surds)

When dealing with square roots or nth roots:

  • Addition/Subtraction: Only “like terms” (same root) can be added or subtracted. Example: 2 root 3 + 5 root 3 = 7 root 3.
  • Multiplication: multiply coefficients together and radicands together. Example: 2 root 3 * 3 root 5 = 6 root 15.
  • Division: Divide coefficients and divide radicands. Example: 10 root 6 / 2 root 2 = 5 root 3.

3. Important Identities

Standard algebraic identities apply to real numbers involving roots:

  • (root a + root b)(root a – root b) = a – b
  • (a + root b)(a – root b) = a^2 – b
  • (root a + root b)^2 = a + 2(root ab) + b

4. Rationalisation

Rationalisation is the process of converting a fraction with an irrational denominator into an equivalent fraction with a rational denominator. This is usually done by multiplying the numerator and denominator by a conjugate (rationalising factor).

Quick Practice Questions

  1. Simplify: (3 + root 3)(2 + root 2)
  2. Rationalise the denominator of 1 / (root 5 + root 2)
  3. Find the value of (64)^(1/2)
  4. Simplify: 7 root 3 – 2 root 3
  5. Evaluate: (root 5 – root 2)^2